Discrete space of size $2 ^ \mathfrak{c}$

spaces/S000219/README.md

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+---
+uid: S000219
+name: Discrete topology on $2^{\mathfrak c}$
+refs:
+  - wikipedia: Discrete_space
+    name: Discrete space on Wikipedia
+---
+
+Let $X=2^{\mathfrak c}$ be the power set of the real numbers,
+and let all subsets of $X$ be open.

spaces/S000219/properties/P000052.md

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+---
+space: S000219
+property: P000052
+value: true
+---
+
+By definition.

spaces/S000219/properties/P000059.md

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+---
+space: S000219
+property: P000059
+value: true
+---
+
+By definition $|X| = 2 ^ \mathfrak{c}$

spaces/S000219/properties/P000163.md

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+---
+space: S000219
+property: P000163
+value: false
+---
+
+By definition $|X| = 2 ^ \mathfrak{c} > \mathfrak{c}$.